Cuboid

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Example of a Template:Nowrap Template:Nowrap hexahedron

In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.Template:R

General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles.Template:R Along with the rectangular cuboids, parallelepiped is a cuboid with six parallelogram faces. Rhombohedron is a cuboid with six rhombus faces. A square frustum is a frustum with a square base, but the rest of its faces are quadrilaterals; the square frustum is formed by truncating the apex of a square pyramid. In attempting to classify cuboids by their symmetries, Template:Harvtxt found that there were at least 22 different cases, "of which only about half are familiar in the shapes of everyday objects".Template:R

There exist quadrilateral-faced hexahedra which are non-convex.

Some notable cuboids
(quadrilateral-faced convex hexahedra • Template:Math vertices and Template:Math edges each)

Image	Name	Faces	Symmetry group
	Cube	Template:Math congruent squares	Template:Math order Template:Math
	Trigonal trapezohedron	Template:Math congruent rhombi	Template:Math order Template:Math
	Rectangular cuboid	Template:Math pairs of rectangles	Template:Math order Template:Math
	Right rhombic prism	Template:Math pair of rhombi, Template:Math congruent squares
	Right square frustum	Template:Math non-congruent squares, Template:Nowrap	Template:Math order Template:Math
	Twisted trigonal trapezohedron	Template:Math congruent quadrilaterals	Template:Math order Template:Math
	Right isosceles-trapezoidal prism	Template:Math pair of isosceles trapezoids; Template:Nowrap	Template:Math order Template:Math
	Rhombohedron	Template:Math pairs of rhombi	Template:Math order Template:Math
	Parallelepiped	Template:Math pairs of parallelograms

See also

• Hypercube
• Lists of shapes